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165E2-F2005 - MA 165 EXAM 2 Fall 2005 ’ Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 2 Fall 2005 ’ Page 1/4 NAME Page 1 10~digit PUID Page 2 Page 3 RECITATION INSTRUCTOR Page 4 RECITATION TIME TOTAL /100 DIRECTIONS 1. OJ Write your name, student ID number, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3 and 4. . The test has four (4) pages, including this one. . Write your answers in the boxes provided. You must show sufficient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. Credit for each problem is given in parentheses in the left hand margin. No books, notes, calculators or any electronic devices may be used on this exam. (16) 1. Find the derivatives of the following functions. (It is not necessary to simplify). (a) y : ell? COSIE (b) y = tam“l x/E (c) f(:c) : \3/1+ tan :13. (d) f($) =1n12x+11 MA 165 EXAM 2 Fall 2005 Page 2 /4 (8) 2. Find an equation of the tangent line to the curve 3/ : emgm) at the point (2,1). (7) 3. Use implicit differentiation to find the slope of the tangent line to the Curve $Z+2$y—y2+$:2 at the point (1,2). (6) 4. Find the value for f(4)(1) (the 4—th derivative evaluated at x 2 1) when f(27) 2 \/2:t — 1. (8) 5. Find the derivative of the function y 2 271”. MA 165 EXAM 2 Fall 2005 Page 3/4 (9) 6. Find the exact value of each expression. . _1 \/§ (a) sm (7) (b) tan‘1 (tan 477’) HUM (c) cos (sin‘1 (—%)) (6) 7. Find the exact value of the derivative of f(:1:) = coshzr when (I; = 1n 2. Write your answer in the form of a ratio of two integers. (b) Use a linear approximation to estimate the number 1n(1.1). 22 ln(1.1) (6) 9. Let f be a function such that f(1) : 3 and f'(1) : 5 (a) Set h(:E) : E. Find h’(1). (b) Let g be the inverse function of f (so that (g o f)(:17) = 3:). Find g'(3). MA 165 EXAM 2 Fall 2005 Page 4/4 (12) 10. A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string have been let out? (12) 11. Two ships, one heading west and the other east, approach each other on parallel courses 8 miles apart. Given that each ship is cruising at 20 miles per hour, at what rate is the distance between them diminishing when they are 10 miles apart? Ship B 8mi Ship A ...
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